Morning Mathematical Monsters & Maniacs!
(Today’s post is sponsored by the letter “M”)
Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.
And what better way to start your week, then by discussing math Monday morning?
So let’s get started this week by discussing Mersenne Prime numbers.
In the finale of Season 17, Marge and Homer Turn a Couple Play (Season 17, Episode 22), the Springfield Isotopes’s star first baseman Buck “Home Run King” Mitchell is having marital problems with his pop star wife Tabitha Vixx (voiced by This Is Us star Mandy Moore). So when he sees Homer and Marge kissing on the Jumbotron, he asks them for advice. But when Homer is later caught giving a neck massage to Tabitha, both couples break up again – and it is hard for Homer and Marge to give advice when they are not talking to each other themselves.
Towards the end of the episode, Tabitha appears on the Jumbotron asking the stadium crowd to guess the evening’s attendance. At first glance, it appears as though the three numbers are just random numbers. However, as you’ll see today and the next couple weeks, these three numbers are more than just random numbers.
8,191
The first number on the Jumbotron is 8,191.
8,191 is a Mersenne prime, named after Marin Mersenne (pictured below), a French Minim friar, who studied them in the early 17th century.
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n.
[Not all numbers of the form 2n − 1 are Mersenne primes, as we’ll see in a few weeks when we look at another number important to the game that bears the form 2n − 1 .]
8,191 is the 5th Mersenne prime. The first 5 Mersenne prime numbers are:
3 = 22 − 1
7 = 23 − 1
31 = 25 − 1
127 = 27 − 1
8,191 = 213 − 1
While the first 4 Mersenne primes were discovered by the Ancient Greeks over 2,300 years ago, 8,191 was not discovered as a prime number until the year 1456. As of this week, there are 51 known Mersenne primes.
Now that we know the secret behind the first number, be sure to come back next week when we talk about the second number.
Do you remember this episode? Did you catch the number 8,191 on the Jumbotron? Did you recognize the number 8,191 as a prime number? Are you familiar with Mersenne primes? Sound off in the comments below. You know we love hearing from you.